Analysis of Particle Transfer for Periodic Lattice Modulation in Three Dimensional Optical Lattice

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We analyze a three dimensional fermion system with an optical lattice and a harmonic confinement potential using the Hubbard model. The dynamical evolution is calculated numerically under the time-dependent Gutzwiller ansatz. The results show that the periodic lattice modulation leads to the particles transfer and to the creation and annihilation of the doublon, which are predominant as the lattice amplitude oscillation becomes larger. In addition, we conclude that the particle transfer is stimulated not by the decrease of the lattice amplitude but rather by the lattice modulation. In cold atom systems, various parameters, such as inter-particle interaction strength and parame- ters of confinement potential, are well controllable experimentally. Some intriguing phenomena such as Mott insulator and antiferromagnetism have been observed in the cold fermion systems with an optical lattice. They can be well described by the Hubbard-model, whose numerical analysis is per- formed in various methods, i.e., Gutzwiller (GW) ansatz, mean-field theory, density matrix renormal- ization group method, quantum Monte Carlo method and so on. The transfer of fermion in the optical lattice is slower than that of boson due to the Pauli blocking. Therefore, the experiments of the Mott insulator transition for fermion systems are more difficult than those for boson ones in general. The theoretical analysis of the linear response (1) for the experiment (2) indicates that the periodic lattice modulation of the optical lattice, which means that the amplitude strength of the lattice changes periodically in time, stimulates the transfer of the particles. Those managements properly make it feasible to more complicated experiments. We analyze a three dimensional system with an optical lattice and a harmonic confinement po- tential using the Hubbard model, and numerically calculate its dynamical evolution under the time- dependent GW ansatz. The cost of numerical calculation for the GW ansatz is lower than those in the other methods, so the GW ansatz is suitable for calculating the realistic three dimensional system. We investigate the time evolution of the particle distribution starting from an spatially inhomo- geneous distribution, when the periodic lattice modulation is applied. The particles transfer is shown for the parameter values of the lattice amplitude oscillation. The relationship between the particle transfer and the oscillation parameters, and the importance of the lattice amplitude oscillation for the particle transfer to the outer sites are discussed from the numerical results. Finally we indicate the method how the particle transfer to the outer sites is promoted so that the Mott insulator transition for fermion can be realized in experiments .